The Dow Jones Industrial Average in the Twentieth Century - Implications for Option Pricing

In this paper, the historical changes in the Dow Jones Industrial Average index are examined. The distributions of index changes over short to moderate length trading intervals are found to have tails that are heavier than can be accounted for by a normal process. This distribution is better represented by a mixture of normal distributions where the mixing is with respect to the index volatility. It is shown that differences in distributional assumptions are sufficient to explain poor performance of the Black-Scholes model and the existence of the volatility smile. The option pricing model presented here is simpler than autoregressive models and is better suited to practical applications